A Twitter spokesperson told CNBC on Monday that the accounts do not violate the company's policies. The company also said it is constantly moderating content on its platform and will take action if it needs to, and that much of the content posted to other platforms doesn't make it to Twitter.

Apple, Facebook and Google-owned YouTube removed videos, pages and podcasts posted by the controversial radio host in a wave of takedowns resulting from violations of company policies. Spotify was among the earliest to remove his podcasts.

Jones took to Twitter and its wholly owned streaming platform Periscope to respond to the bans Monday.